Estimating the dimensionality of complex networks using persistent homology

Abstract

[en] In this work, a new interdisciplinary approach is presented to study the dimensionality of complex networks using techniques from topological data analysis (TDA) through a filtration of graphs by vertex degrees. For each of two real-world complex networks, 30 surrogate graphs were generated in each dimension from 1 to 10, and several TDA descriptors of graphs were compared with the corresponding values for the real networks in order to estimate their latent dimension. Total persistence, Wasserstein distance and scale-space kernel dissimilarity, among other descriptors, yielded consistent outcomes. The results of this study suggest that TDA is sensible to the latent dimension of complex networks, and provide conclusions consistent with those obtained in previous studies.